BIMSA >
BIMSA-Tsinghua Seminar on Computational Discrete Global Geometry Structures, Topology Materials and Quantum Computer
Rigidity and deformation of discrete conformal structures on polyhedral surfaces
Rigidity and deformation of discrete conformal structures on polyhedral surfaces
Organizers
Zheng Wei Liu
, Shing-Tung Yau
, Hui Zhao
Speaker
Xu Xu
Time
Friday, April 8, 2022 2:00 PM - 3:30 PM
Online
Tencent 494 085 7642
(2022)
Abstract
Discrete conformal structure is a discrete analogue of the smooth conformal structure on manifolds, which assigns the discrete metrics by scalar functions defined on the vertices. There are special types of discrete conformal structures that have been extensively studied on surfaces in the history, including the tangential circle packing, Thurston's circle packing, inversive distance circle packing and vertex scaling. In this talk, we will discuss some recent progresses on the rigidity and deformation of generic discrete conformal structures on surfaces. Some open problems related to generic discrete conformal structures on surfaces will also be discussed. If time permits, we will sketch a proof of Glickenstein’s conjecture on the rigidity of generic discrete conformal structures on polyhedral surfaces, which includes Luo's conjecture on the rigidity of vertex scaling and Bowers-Stephenson's conjecture on the rigidity of inversive distance circle packings on polyhedral surfaces as special cases.
[1] X. Xu, Rigidity and deformation of discrete conformal structures on polyhedral surfaces, arXiv:2103.05272v2 [math.DG].
[2] X. Xu, Rigidity of inversive distance circle packings revisited, Adv. Math. 332 (2018), 476-509.
[3] T. Wu, X. Xu, Fractional combinatorial Calabi flow on surfaces, arXiv:2107.14102 [math.GT].
Speaker Intro
徐旭，武汉大学副教授，2006年本科毕业于华中科技大学，2011年在中国科学院数学研究所获得博士学位，2011年07月加入武汉大学数学与统计学院任教至今。研究领域为离散几何与微分几何，证明了三维流形上堆球度量的整体刚性、曲面上反演距离大于-1时反演距离堆圆度量的刚性、曲面上一般形式离散共形结构的刚性，还在预定组合曲率问题和组合曲率流相关问题上取得了系列进展。